Euclid's Elements of Geometry: From the Latin Translation of Commandine. To which is Added, a Treatise of the Nature and Arithmetic of Logarithms ; Likewise Another of the Elements of Plain and Spherical Trigonometry : with a Preface ...T. Woodward, 1723 - 364 páginas |
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Página
... produces Tediousness and Confufion . On thefe Accounts principally , it was that I undertook to publish the first fix Books of Euclid , with the 11th and 12th , according to Commandinus's Edition ; the reft I forbore , because those ...
... produces Tediousness and Confufion . On thefe Accounts principally , it was that I undertook to publish the first fix Books of Euclid , with the 11th and 12th , according to Commandinus's Edition ; the reft I forbore , because those ...
Página 6
... produce DA and DC directly forwards to E and C + about the Center C , with the Distance B C , de- fcribe the Circle BGH * ; and about the Center D , with the Distance DG , defcribe the Circle G KL . Poft . 3 . + Def . * Now because the ...
... produce DA and DC directly forwards to E and C + about the Center C , with the Distance B C , de- fcribe the Circle BGH * ; and about the Center D , with the Distance DG , defcribe the Circle G KL . Poft . 3 . + Def . * Now because the ...
Página 8
... produced , the Angles under the Base shall be equal be- tween themselves . LE ET ABC be an Ifofceles Triangle , having the Side A B equal to the Side A C ; and let the equal Sides AB , AC , be produced directly forwards to D and E. I ...
... produced , the Angles under the Base shall be equal be- tween themselves . LE ET ABC be an Ifofceles Triangle , having the Side A B equal to the Side A C ; and let the equal Sides AB , AC , be produced directly forwards to D and E. I ...
Página 9
... produced , the Angles under the Bafe will be alfo equal between themselves . Coroll . Hence every Equilateral Triangle is alfo Equi- angular . PROPOSITION VI . THEOREM . If two Angles of a Triangle be equal , then the Sides fub- tending ...
... produced , the Angles under the Bafe will be alfo equal between themselves . Coroll . Hence every Equilateral Triangle is alfo Equi- angular . PROPOSITION VI . THEOREM . If two Angles of a Triangle be equal , then the Sides fub- tending ...
Página 17
... produced , the outward Angle is greater than either of the inward Oppofite Angles . LE ET ABC be a Triangle , and one of its Sides BC , be produced to D. I fay , the outward Angle ACD is greater than either of the inward Angles CBA , or ...
... produced , the outward Angle is greater than either of the inward Oppofite Angles . LE ET ABC be a Triangle , and one of its Sides BC , be produced to D. I fay , the outward Angle ACD is greater than either of the inward Angles CBA , or ...
Términos y frases comunes
alfo equal alſo Angle ABC Angle BAC Baſe becauſe bifected Center Circle ABCD Circle EFGH Circumference Cofine Cone confequently contain'd Coroll Cylinder defcrib'd defcribed demonftrated Diameter Diſtance drawn thro equal Angles equiangular equilateral Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reafon fecond fhall be equal fimilar fince firft firſt folid Parallelepipedon fome fore ftand fubtending given Right Line Gnomon greater join leffer lefs likewife Logarithm Magnitudes Meaſure Number paffing thro Parallelogram perpendicular Polygon Prifm Priſms Prop PROPOSITION Pyramid Quadrant Ratio Rectangle remaining Angle Right Angles Right Line A B Right Line AB Right-lin'd Figure Right-lin❜d Segment ſhall Sine Solid Sphere Subtangent thefe THEOREM theſe thofe Triangle ABC triplicate Proportion Unity Vertex the Point Wherefore whofe Bafe whole
Pasajes populares
Página 190 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 160 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Página 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Página 152 - ... therefore the angle DFG is equal to the angle DFE, and the angle at G to the angle at E : but the angle DFG is equal to the angle ACB...
Página 100 - About a given circle to describe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to describe a triangle about the circle ABC equiangular to the triangle DEF.
Página 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Página 210 - CD; therefore AC is a parallelogram. In like manner, it may be proved that each of the figures CE, FG, GB, BF, AE, is a parallelogram...
Página 229 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.
Página 164 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.
Página 93 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.